1. The confinement of electrons to a particular atom in a molecule or to a particular chemical bond.
2. In the theory of disordered solids, the concept that an electron is concentrated around a specific site and cannot contribute to the solid's electrical conductivity (at absolute zero) by moving through the system. In one dimension any amount of disorder makes all electron states localized. In three dimensions a small amount of disorder makes electron states near the top and the bottom of the energy bands localized; states in the centre of the bands are called extended states because they can propagate through the system and hence contribute to electrical conductivity. The dividing energies between localized and extended states are called mobility edges. Given sufficient disorder all states become localized. In two dimensions all electron states in disordered solids are thought to be localized, with some states being strongly localized around specific sites while other states are weakly localized around specific sites. Localization also occurs in disordered solids for other excitations, such as phonons and spin waves.